Problem: Kevin is 4 years younger than Stephanie. For the last two years, Stephanie and Kevin have been going to the same school. Seven years ago, Stephanie was 5 times as old as Kevin. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Stephanie and Kevin. Let Stephanie's current age be $s$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $s = k + 4$ Seven years ago, Stephanie was $s - 7$ years old, and Kevin was $k - 7$ years old. The information in the second sentence can be expressed in the following equation: $s - 7 = 5(k - 7)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = s - 4$ . Substituting this into our second equation, we get the equation: $s - 7 = 5($ $(s - 4)$ $ -$ $ 7)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 7 = 5s - 55$ Solving for $s$ , we get: $4 s = 48$ $s = 12$.